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Re: rand("state")


From: Francesco Potorti`
Subject: Re: rand("state")
Date: Thu, 16 Feb 2006 18:41:38 +0100

>Thinking about it a little more - the entire pseudorandom sequence has a 
>length of about 4*10^6001, so if you are making numerous sequences of 
>length 10^9 say, the probability that two or more are overlapping is 
>always extremely small (assuming that the starting point in the sequence 
>is always selected at random from all possible starting points).

You just sent a calculation that can be used as the base to compute the
probability of having non-overlapping sequences, given the number of
sequences, their length, and the generator period, under the assumption
of uniformly choosing a random starting point for each sequence.

I did not check it, but yes, it can be seen as an instance of a birthday
problem.

Or else you can see it as this: have a generator of period P, from which
you have already taken N non-overlapping sequences of length L.  The
probability that one more sequence of lenght L starting from a random
point does not overlap with one of the already taken N sequences is
equal to the probability that no taken sequence starts in an interval
of length 2*L, that is, (1-N/P)^(2*L), under the assumption that N*L<<P,
which is true in our case.

If what I wrote is correct, then you have the probability of choosing a
new good sequence, given that you have already chosen N.

-- 
Francesco Potortì (ricercatore)        Voice: +39 050 315 3058 (op.2111)
ISTI - Area della ricerca CNR          Fax:   +39 050 313 8091
via G. Moruzzi 1, I-56124 Pisa         Email: address@hidden
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